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2 results found for "conjugate roots" in Class 10.

Question Hard Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 26

निम्न में से कौन सा बहुपद परिमेय गुणांकों वाला है और जिसके शून्यक \(1+\sqrt{2}\) तथा \(1-\sqrt{2}\) हैं?

Which polynomial has rational coefficients and zeroes \(1+\sqrt{2}\) and \(1-\sqrt{2}\)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-2x-1\)

Step 1

Concept

The sum is (2) and the product is (1-2=-1), so the polynomial is \(x^2-2x-1\). Keep signs correct in exams.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-2x-1\). The sum is (2) and the product is (1-2=-1), so the polynomial is \(x^2-2x-1\). Keep signs correct in exams.

Step 3

Exam Tip

योग (2) और गुणनफल (1-2=-1), इसलिए बहुपद \(x^2-2x-1\) है। परीक्षा में चिन्हों को ठीक रखें।

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Question Hard Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 28

यदि \(2+\sqrt{3}\) एक बहुपद \(x^2-4x+1\) का शून्यक है, तो दूसरा शून्यक क्या होगा?

If \(2+\sqrt{3}\) is a zero of the polynomial \(x^2-4x+1\), what is the other zero?

Explanation opens after your attempt
Correct Answer

A. \(2-\sqrt{3}\)

Step 1

Concept

For a quadratic with rational coefficients, if \(a+\sqrt{b}\) is a zero then \(a-\sqrt{b}\) is also a zero. The conjugate-root rule is useful in exams.

Step 2

Why this answer is correct

The correct answer is A. \(2-\sqrt{3}\). For a quadratic with rational coefficients, if \(a+\sqrt{b}\) is a zero then \(a-\sqrt{b}\) is also a zero. The conjugate-root rule is useful in exams.

Step 3

Exam Tip

परिमेय गुणांकों वाले द्विघात में \(a+\sqrt{b}\) के साथ \(a-\sqrt{b}\) भी शून्यक होता है। परीक्षा में संयुग्मी मूल का नियम उपयोगी है।

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